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Whitman Mission NHS - For Kids
  
 

JACK'S MATH

Jack was a ranger at Whitman Mission for nearly 30 years. He knew about the out-of-doors, including how to measure trees, rivers, and ponds. You can use the same techniques he used to measure trees or ponds at your home or local park. Or you can come to Whitman Mission and measure things here. So try your hand at measuring the natural world and have fun.

Measuring Distance

Measuring Length

Measuring Width

Measuring Height

Measuring Slope

Measuring Water Flow

Measuring Area by Pacing

Measuring Trees: Circumference, Diameter, Volume, and Board Feet

MEASURING DISTANCE

One way of measuring distances is by counting your paces. But you need to know the length of your pace first.

Measuring Your Pace
  1. Mark off 50 feet on the ground.
  2. Starting with your toes on a starting line, pace the distance 10 times, counting the steps.
  3. Divide the total paces by ten.
    125 paces
    10 times = 12.5 paces (average)

    125 paces--divided by--10 times--equals--12.5 paces (average)
  4. Divide 50 feet by average paces. This is your length of pace.
    50 feet
    12.5 paces = 4 foot pace

    50 feet--divided by--12.5 paces--equals--4 foot pace



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MEASURING LENGTH


You can use parts of your body to estimate the length of objects, if you know how long your different parts are.

Personal Measurements

Name____________________________________________ Date_____________________

Address___________________________________________ Age_____________________

My height is ___________ feet, ___________ inches

My eyes are ____________ feet, ___________ inches above the ground.

My reach across, from tip of one outstretched hand to the tip of the other, is ____________ feet, __________ inches.

The length of my forearm, from tip of little finger to elbow, is _______ feet, __________inches.

My hand span, from thumb to little finger, is ___________ inches.

The breadth of my thumb is __________ inches.

The length of my index finger is __________ inches.

The length of my foot is __________ inches.

The length of my pace is __________ feet.

Distance from my __________ to __________ is exactly one inch.**

Distance from my __________ to __________ is exactly one foot.

Distance from my __________ to __________ is exactly one yard.


**Example: End of thumb to first joint. Must be determined for each individual.



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MEASURING WIDTH


Pacing Method

Pacing method.
  1. Note a landmark (a) on the other side of pond. Place a stick (b) where you are, exactly opposite the landmark.
  2. Stand at stick and pace off 100' at a right angle to line (a-b). At this point place another stick (c).
  3. Continue pacing along this line for half as much distance as before (in this case 50'). Place another stick (d).
  4. Make another right angle and walk until you can sight stick (c) and the landmark (a) in a straight line, then stop. With another stick mark this point (e).
  5. Now line (d-e) is half the distance across the pond. Pace line (d-e). Multiply line (d-e) by two. This is the approximate distance across the pond (line a-b).
  6. Replace sticks or rocks to where you found them.



Compass Method
Compass method.

Walk West until point (a) is exactly Northeast.

Sight compass North in line with tree.


  1. Point compass North. Take compass reading across pond on landmark (a). (In example above North is across the pond). Place stick at point (b).

  2. Turn (90 degrees) on the compass (in example this is a West). Now walk until the compass is halfway between the reading at point (ab) and the reading on the line you are now proceeding (b-c). (In the example this is NE.)

  3. At this point (c), line (bc)=line (a-b). So pace distance of line (b-c) and this is the distance across the pond.



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MEASURING HEIGHT

Indian Method
  1. Walk away from the tree, bend over and sight its top between your legs. When you can see the top of the tree while in this position, stop.
  2. The approximate height of the tree will equal your distance from the tree. In bending over, grasp your knees or your ankle.


Stick Methods
  1. Mark your height on the tree trunk.
  2. Step back several spaces. Hold a stick up before you in an outstretched hand. Sight the height of your mark on the tree and mark this on the stick with your thumbnail.
  3. See how many times this height goes up the tree. Multiply the number of times by your height. This is the approximate height of the tree.


Shadow Method
Shadow method.


Formula:
Length of tree shadow (ab) X Height of stick
Length of stick shadow (cd)
= height of tree

(Length of tree shadow [ab]--divided by--Length of stick shadow [cd]--times --Height of stick--equals--Height of tree).



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MEASURING SLOPE

Measuring slope.
  1. Percent of slope is the number of units the land falls or rises in 100 units of horizontal distance.
  2. To measure percent of slope use a stick 50" long and a level, or bottle with water and a yardstick.
  3. Hold yardstick in upright position. Place 50" stick on slope and raise free end until it is level. Note its distance above the ground.
  4. Read this distance in inches and multiply by two to get percent of slope.


**By knowing slope of land you can judge what the best use of the land could be (farming, contour farming, pasture, wildlife, etc...) Get land use designations from Soil Conservation office.



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MEASURING WATER FLOW *

To calculate the volume and/or rate of flow for a stream requires several measurements and equations:
  1. L (length) = feet
  2. W (average width) = feet
  3. D (average depth) = feet
  4. V (total volume) = L x W x D = cubic feet
  5. T (time for float to travel L) = second
  6. Rate of flow = L/T = ft. per second
  7. Discharge = V/T = cubic feet per second
* Care should be taken around rivers and streams. Children should be supervised. This is for personal safety and for the well being of the stream.



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MEASURING AREA BY PACING


Mission and Emigrant House.


  1. By pacing, find the perimeter of each house.
  2. How do they compare? Which would have the most living space?






Blacksmith Shop
Blacksmith Shop.
  1. By pacing, find the square footage of the blacksmith shop.
  2. Find sqare footage of the left hand room.
  3. Eight people lived in this room. How many sqare feet did each person have to live in?



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MEASURING CIRCUMFERENCE, DIAMETER, VOLUME AND BOARD FEET OF A TREE

  1. Circumference: Use a tape measure. Measure around the tree at breast height.
  2. Diameter: On the back of your tape measure, mark a line 3.14 inches from end of tape. Put a 1" mark there. From that mark, make another mark 3.14 inches farther down and place a 2" mark there. Continue doing this to the end of the tape. Each 3.14 mark represents one inch in tree diameter.
  3. Volume: Volume of a cone equals 1.047--times--radius squared--times--height
    or
    pi--divided by--three--times--radius squared--times--height
  4. Board feet: One board is a piece of lumber 1 inch thick, 12 inches wide and 12 inches long. This equals to 144 cubic inches. To find the total board feet in a tree, you divide volume in inches by 144 cubic inches.

    Volume in inches = Board feet in inches
    144 cubic inches (Volume in inches--divided by--144 cubic inches--equals --Board feet in inches).

    This is the approximate total board feet in the tree. Usable or merchantable board feet is considerably less. You can get a volume table from the Forest Service. The Forest Service table gives you the volume according to the number of usable logs. Usable logs are 16 foot sections. So you would need to divide the tree height into the number of 16 ft. sections in your tree in order to use the table.



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Last modified on: January 31, 2004

 

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